Question: $\overline{AB}$ = $10$ $\overline{AC} = {?}$ $A$ $C$ $B$ $10$ $?$ $ \sin( \angle ABC ) = \dfrac{4}{5}, \cos( \angle ABC ) = \dfrac{3}{5}, \tan( \angle ABC ) = \dfrac{4}{3}$
Solution: $\overline{AB}$ is the hypotenuse $\overline{AC}$ is opposite to $\angle ABC$ SOH CAH TOA We know the hypotenuse and need to solve for the opposite side so we can use the sine function (SOH) $ \sin( \angle ABC ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{\overline{AC}}{\overline{AB}}= \frac{\overline{AC}}{10} $ Since we have already been given $\sin( \angle ABC )$ , we can set up a proportion to find $\overline{AC}$ $ \sin( \angle ABC ) = \dfrac{4}{5} = \frac{\overline{AC}}{10}$ Simplify. $\overline{AC} = 8$